Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
Step-by-step explanation:
Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
Answer:
1. her elevation at noon was 3 meters
2. (-2, 7)
3. (1, 0)
Step-by-step explanation:
1. when x = 0, it is noon, y = 3 when x is 7
2. when x = -2 it is 10 am because when x is 0, it is noon, or 12 pm, her elevation is 7 meters above sea level
3. when x is 1, it is 1 pm, and her elevation is 0 meters
Sqrt(x+4-3)=1
sqrt (x+1) = 1
x+1 = 1^2
x=1-1
x=0
This is how you would get x=0
Hope I helped :)
It is 2i I standing for imaginary since it is a negative
square root of -1×4
4 square rooted is 2
and a negative number square rooted is i
